Foundations Of Rigid Geometry I PDF Download
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Author | : Kazuhiro Fujiwara |
Publisher | : |
Total Pages | : 863 |
Release | : 2018 |
Genre | : MATHEMATICS |
ISBN | : 9783037196359 |
Download Foundations of Rigid Geometry I Book in PDF, ePub and Kindle
Rigid geometry is one of the modern branches of algebraic and arithmetic geometry. It has its historical origin in J. Tate's rigid analytic geometry, which aimed at developing an analytic geometry over non-archimedean valued fields. Nowadays, rigid geometry is a discipline in its own right and has acquired vast and rich structures, based on discoveries of its relationship with birational and formal geometries. In this research monograph, foundational aspects of rigid geometry are discussed, putting emphasis on birational and topological features of rigid spaces. Besides the rigid geometry itself, topics include the general theory of formal schemes and formal algebraic spaces, based on a theory of complete rings which are not necessarily Noetherian. Also included is a discussion on the relationship with Tate's original rigid analytic geometry, V.G. Berkovich's analytic geometry and R. Huber's adic spaces. As a model example of applications, a proof of Nagata's compactification theorem for schemes is given in the appendix. The book is encyclopedic and almost self-contained.
Author | : Kazuhiro Fujiwara |
Publisher | : |
Total Pages | : 0 |
Release | : 2018 |
Genre | : |
ISBN | : |
Download Foundations of Rigid Geometry Book in PDF, ePub and Kindle
Author | : Siegfried Bosch |
Publisher | : Springer |
Total Pages | : 255 |
Release | : 2014-08-22 |
Genre | : Mathematics |
ISBN | : 3319044176 |
Download Lectures on Formal and Rigid Geometry Book in PDF, ePub and Kindle
The aim of this work is to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work. This Lecture Notes Volume is a revised and slightly expanded version of a preprint that appeared in 2005 at the University of Münster's Collaborative Research Center "Geometrical Structures in Mathematics".
Author | : Werner Lütkebohmert |
Publisher | : Springer |
Total Pages | : 398 |
Release | : 2016-01-26 |
Genre | : Mathematics |
ISBN | : 331927371X |
Download Rigid Geometry of Curves and Their Jacobians Book in PDF, ePub and Kindle
This book presents some of the most important aspects of rigid geometry, namely its applications to the study of smooth algebraic curves, of their Jacobians, and of abelian varieties - all of them defined over a complete non-archimedean valued field. The text starts with a survey of the foundation of rigid geometry, and then focuses on a detailed treatment of the applications. In the case of curves with split rational reduction there is a complete analogue to the fascinating theory of Riemann surfaces. In the case of proper smooth group varieties the uniformization and the construction of abelian varieties are treated in detail. Rigid geometry was established by John Tate and was enriched by a formal algebraic approach launched by Michel Raynaud. It has proved as a means to illustrate the geometric ideas behind the abstract methods of formal algebraic geometry as used by Mumford and Faltings. This book should be of great use to students wishing to enter this field, as well as those already working in it.
Author | : Jean Fresnel |
Publisher | : Springer Science & Business Media |
Total Pages | : 303 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461200415 |
Download Rigid Analytic Geometry and Its Applications Book in PDF, ePub and Kindle
Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "points of rigid spaces," étale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.
Author | : André Weil |
Publisher | : |
Total Pages | : 363 |
Release | : 1946 |
Genre | : Geometry, Algebraic |
ISBN | : 9781470431761 |
Download Foundations of Algebraic Geometry Book in PDF, ePub and Kindle
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Author | : Vladimir G. Berkovich |
Publisher | : American Mathematical Soc. |
Total Pages | : 181 |
Release | : 2012-08-02 |
Genre | : Mathematics |
ISBN | : 0821890204 |
Download Spectral Theory and Analytic Geometry over Non-Archimedean Fields Book in PDF, ePub and Kindle
The purpose of this book is to introduce a new notion of analytic space over a non-Archimedean field. Despite the total disconnectedness of the ground field, these analytic spaces have the usual topological properties of a complex analytic space, such as local compactness and local arcwise connectedness. This makes it possible to apply the usual notions of homotopy and singular homology. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of Bruhat-Tits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space. Geometrical considerations are used to obtain some applications, and the analytic spaces are used to construct the foundations of a non-Archimedean spectral theory of bounded linear operators. This book requires a background at the level of basic graduate courses in algebra and topology, as well as some familiarity with algebraic geometry. It would be of interest to research mathematicians and graduate students working in algebraic geometry, number theory, and -adic analysis.
Author | : Tim Maudlin |
Publisher | : |
Total Pages | : 374 |
Release | : 2014-02 |
Genre | : Mathematics |
ISBN | : 0198701306 |
Download New Foundations for Physical Geometry Book in PDF, ePub and Kindle
Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Author | : D. Hestenes |
Publisher | : Springer Science & Business Media |
Total Pages | : 655 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9400948026 |
Download New Foundations for Classical Mechanics Book in PDF, ePub and Kindle
This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applica tions matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities. This book covers the fairly standard material for a course on the mechanics of particles and rigid bodies. However, it will be seen that geometric algebra brings new insights into the treatment of nearly every topic and produces simplifications that move the subject quickly to advanced levels. That has made it possible in this book to carry the treatment of two major topics in mechanics well beyond the level of other textbooks. A few words are in order about the unique treatment of these two topics, namely, rotational dynamics and celestial mechanics.
Author | : Ofer Gabber |
Publisher | : Springer Science & Business Media |
Total Pages | : 324 |
Release | : 2003 |
Genre | : Arithmetical algebraic geometry |
ISBN | : 9783540405948 |
Download Almost Ring Theory Book in PDF, ePub and Kindle